Handling vacuum regions in a hybrid plasma solver

In a hybrid plasma solver (particle ions, fluid mass-less electrons) regions of vacuum, or very low charge density, can cause problems since the evaluation of the electric field involves division by charge density. This causes large electric fields in low density regions that can lead to numerical instabilities. Here we propose a self consistent handling of vacuum regions for hybrid solvers. Vacuum regions can be considered having infinite resistivity, and in this limit Faraday's law approaches a magnetic diffusion equation. We describe an algorithm that solves such a diffusion equation in regions with charge density below a threshold value. We also present an implementation of this algorithm in a hybrid plasma solver, and an application to the interaction between the Moon and the solar wind. We also discuss the implementation of hyperresistivity for smoothing the electric field in a PIC solver.